Proportion Calculator
Solve A/B = C/X — find the missing value in any proportion
Proportion Calculator
Solve A/B = C/X for the unknown value
If A/B = C/X, enter A, B, and C to find X
X = (B x C) / AWhat is a Proportion Calculator?
A Proportion Calculator is a math tool that helps you solve problems where two ratios are equal. A proportion is written like a:b = c:d or a/b = c/d.
Proportions are used when you want to scale values up or down while keeping the same relationship. This comes up in everyday situations like resizing recipes, converting map scales, mixing solutions, comparing prices, and solving "missing value" problems such as "If 3 items cost $12, how much do 5 items cost?"
This calculator makes it easy to find the unknown value in a proportion (often represented as x) and reduces mistakes from manual cross-multiplication.
How to Use This Proportion Calculator
- Enter the known values -- in the proportion (for example: a, b, and c)
- Leave the unknown value blank -- (or enter x) if your calculator supports it
- Confirm the proportion format -- common formats include a/b = c/d or a:b = c:d
- Click "Calculate" -- to solve for the missing value
- Review the result -- and make sure it makes sense for the problem (especially units)
Tips:
- Keep units consistent (don't mix inches and feet without converting first)
- Proportions assume the relationship is constant—if the relationship changes (discounts, fees, non-linear growth), a simple proportion won't apply
- Double-check that you placed numbers on the correct side (swapping values can change the result)
Proportion Formulas
Basic Proportion
a / b = c / d
Two ratios are equal
Cross-Multiplication Rule
Multiply diagonally across the equals sign:
a × d = b × c
Both fractions represent the same value, so their cross-products must match
Solving for a Missing Value
Solve for d
a/b = c/d
d = (b × c) / a
Solve for c
a/b = c/d
c = (a × d) / b
Solve for b
a/b = c/d
b = (a × d) / c
Solve for a
a/b = c/d
a = (b × c) / d
Example Calculations
Example 1: Solve for x in a Simple Proportion
Proportion: 2/5 = x/20
Cross-multiply: 2 × 20 = 5 × x → 40 = 5x
Solve: x = 40 ÷ 5 = 8
Result: x = 8
Example 2: Price Scaling
Problem: If 3 notebooks cost $12, how much do 5 notebooks cost?
Proportion: 3/12 = 5/x
Cross-multiply: 3x = 12 × 5 = 60
Solve: x = 60 ÷ 3 = 20
Result: $20
Example 3: Recipe Scaling
Problem: A recipe uses 4 cups of flour for 10 servings. How much flour for 25 servings?
Proportion: 4/10 = x/25
Cross-multiply: 4 × 25 = 10x → 100 = 10x
Solve: x = 10
Result: 10 cups of flour
Example 4: Map Scale Conversion
Problem: A map scale says 1 inch = 8 miles. If two towns are 3.5 inches apart, what is the real distance?
Proportion: 1/8 = 3.5/x
Cross-multiply: 1 × x = 8 × 3.5
Solve: x = 28
Result: 28 miles
Frequently Asked Questions
What is a proportion in simple terms?
A proportion states that two ratios are equal. It's a way to say "these two relationships match," like 2/3 = 4/6.
What is cross-multiplication, and why does it work?
Cross-multiplication means multiplying diagonally across the proportion: a/b = c/d becomes a×d = b×c. It works because both fractions represent the same value, so their cross-products must match.
When should I use a proportion calculator?
Use it when a relationship is constant—common cases include scaling recipes, unit conversions, mixture ratios, map scales, and "cost per item" problems.
What mistakes cause wrong answers in proportions?
Common mistakes include mixing units, placing numbers in the wrong positions, forgetting that the relationship must be constant, or including extra factors like fixed fees or discounts that break proportionality.
What's the difference between ratio and proportion?
A ratio compares quantities (like 3:2). A proportion states that two ratios are equal (like 3:2 = 12:8). Proportions are often used to solve for unknown values.
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What Is a Proportion?
A proportion is an equation stating that two ratios are equal: A/B = C/D. Given any three of the four values, you can solve for the fourth using cross-multiplication. Proportions are fundamental in everyday life — from cooking (scaling recipes up or down) and maps (converting scale distances to real distances) to finance (currency exchange) and geometry (similar triangles where corresponding sides are proportional).
This calculator solves for the missing fourth value instantly. Enter any three known values and leave the fourth blank — the tool applies cross-multiplication to find X. It handles both direct proportions (where quantities increase together at the same rate) and inverse proportions (where one quantity increases as the other decreases, like speed and travel time for a fixed distance).
How to Use the Proportion Calculator
- Enter three of the four values in the proportion A/B = C/X.
- Leave the unknown value blank or mark it as X.
- Click Calculate.
- Read the solved value for X in the result field.
Proportion Formulas
Direct proportion: A/B = C/X → X = (B × C) / A
Cross-multiplication:
A × X = B × C
X = (B × C) / A
Inverse proportion: A × B = C × X → X = (A × B) / C
Example (recipe scaling):
2 cups flour for 12 cookies → ? cups for 30 cookies
2/12 = X/30 → X = (30 × 2) / 12 = 5 cupsIn a direct proportion, as one quantity increases, the other increases at the same rate. In an inverse proportion, as one quantity increases, the other decreases proportionally — their product stays constant.
Real-World Examples
Map Scale
A map uses a scale of 1 cm = 5 km. If two cities are 3.5 cm apart on the map, the real distance is: 1/5 = 3.5/X → X = (5 × 3.5) / 1 = 17.5 km.
Recipe Scaling
A recipe calls for 3 eggs to make 24 cupcakes. How many eggs do you need for 40 cupcakes? 3/24 = X/40 → X = (40 × 3) / 24 = 5 eggs.
Speed and Time (Inverse Proportion)
At 60 km/h a trip takes 2 hours. At 120 km/h (twice as fast), the time halves: 60 × 2 = 120 × X → X = (60 × 2) / 120 = 1 hour. Speed and time are inversely proportional for a fixed distance.